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1.3 Ray sampling (10 points)

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1.4 Point Sampling (10 points)

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1.5 Volume Rendering (30 points)

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2.2 Loss and training (5 points)

The center of the box and the side lengths of the box after training are (0.25, 0.25, 0.00) and (2.01, 1.50, 1.50), respectively.

2.3. Visualization

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3. Optimizing a Neural Radiance Field (NeRF) (30 points)

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4.3 High Resolution Imagery (10 points)

This high resolution image was rendered from a view-independent NeRF with a MLP with 9 hidden layers, each with a dimension of 128. The color and density at each point was regressed with a linear layer that takes in the output of the final hidden layer as input and outputs 4 values. 256 points were sampled along each ray for volume rendering. We use the same values as Q3 for all other hyperparameters, including the embedding dimensions of the fourier embeddings for the xyz coordinates and ray direction inputs. The following rendered image shows that while sampling more rays (pixels), more points along each ray, and using a higher capacity network may increase the resolution of the rendering, it fails to reconstruct the distinct bumps of the lego blocks. This is most likely due to the fact that we're not using enough dimensions in the fourier embeddings, limiting the ability of the network to model high-frequency details.

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